Reversibility of quantum resources through probabilistic protocols

TL;DR

This paper demonstrates that all quantum resource states can be reversibly transformed using probabilistic protocols, establishing a fundamental link between transformation rates and resource measures in quantum information theory.

Contribution

It proves the possibility of asymptotic reversibility of quantum resources via probabilistic protocols, extending previous incomplete results and establishing optimal transformation sets.

Findings

Reversible interconversion of quantum resource states is achievable probabilistically.

Success probability of transformations can be bounded away from zero asymptotically.

Connection established between probabilistic transformation rates and strong converse rates.

Abstract

Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating, and we show that this choice is optimal: smaller sets of transformations cannot lead to reversibility. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations, which we strengthen into an exact equivalence in the case of entanglement distillation.